eli5 / How do we know the half life of (or even that it is radioactive) Bismuth-209 when it is literally longer than the age of the universe by several orders of magnitude
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You can calculate the half-life of a substance by measuring the rate at which it decays. Bismuth-209 decays by releasing alpha particles, which is a Helium nucleus – two neutrons and two protons.
In 2003 scientists at Institut d’Astrophysique Spatiale in France took a sample of Bismuth-209 and connected it to a very sensitive detector, and measured how many alpha particles it released over the course of 5 days. If you know the mass you started with, you know how many atoms you had, and if you know how many alpha particles were released, you know how many of those atoms underwent decay. You can extrapolate from that to know how long it would take for half of the atoms in the sample to decay, and that’s your half-life.
In the case of the Bismuth-209 experiment, they had something like 128 alpha particles, total, from 100 grams of the substance. Considering that’s like 3×10^23 atoms, and only 128 of them underwent decay in 5 days, that’s an extremely tiny fraction of the sample. Hence it having a half life of 10^19 years.
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